Two parts of this talk

1. Increasing “um”: a language change in progress
2. How informative is it?

UhUm Package

The raw data from the Philadelphia Neighborhood Corpus available here:

  library(devtools)

  install_github("jofrhwld/UhUm")

UhUm Package

  library(UhUm)
  head(um_PNC, 3)

##    idstring word start_time end_time vowel_start vowel_end nasal_start
## 1 PH00-1-1-   UH      24.39    24.69       24.39     24.69          NA
## 2 PH00-1-1-   UH      34.96    35.24       34.96     35.24          NA
## 3 PH00-1-1-   UM      37.90    38.27       37.90     38.12       38.12
##   nasal_end next_seg next_seg_start next_seg_end chunk_start chunk_end
## 1        NA        S          24.69        24.87       24.39     25.29
## 2        NA        F          35.24        35.35       34.96     37.11
## 3     38.27       sp          38.27        38.39       37.90     38.80
##   nwords sex year age ethnicity schooling transcribed total nvowels
## 1   6551   m 2000  21       i/r        14        2811  2814    3078
## 2   6551   m 2000  21       i/r        14        2811  2814    3078
## 3   6551   m 2000  21       i/r        14        2811  2814    3078

um_PNC

  um_PNC%>%
    group_by(word, sex)%>%
    summarise(n = n())%>%
    ungroup()%>%
    spread(sex, n)

## Source: local data frame [5 x 3]
## 
##     word    f    m
## 1 AND_UH  904 1176
## 2 AND_UM  314  153
## 3     UH 7523 9520
## 4     UM 4132 1792
## 5  UM_UH    7    2

Transcription

From the FAVE transcription guidelines:

Um Increasing

Um Increasing

Filled Pauses

Flat (or decreasing?)

Cohorts

Filled Pause Rate

Cohorts

Conditioning Factors

Conditioning Factors

Constant Rate Effect Modelling

CRE Modelling

Conditioning Factors

Following Pause

Following Pause

Following Pause

Following Pause

## Warning: Removed 19 rows containing missing values (stat_smooth).
## Warning: Removed 53 rows containing missing values (stat_smooth).

Following Pause

## is_um ~ decade * log2dur + (1 | idstring)
## <environment: 0x7fb2cddf1918>

This would be weird:

\[\text{fp}\rightarrow\text{ə}\left<\begin{array}{c}\text{m}\\\emptyset\end{array}\right>\]

Variation

Variation

Persistence, from Tamminga (2014)

Conditional Probabilities

Linguists have written about:

• \(p =P(\text{um}~|~\text{gender})\)

Someone else has written about(?):

• \(q = P(\text{gender}~|~\text{ukip})\)

Conditional Probabilities

\(P(\text{ukip}~|~\text{um}) = \mathcal{M}(p,q) \approx 1\)

• \(\mathcal{M}(x)=\) the media bollocks fuction

Is this a signal?

Mutual information

Hang 1 lamp if the British are coming by land, 2 if by sea.

• \(P(\text{1 lamp}~|~\text{land})=1\)
• \(P(\text{2 lamps}~|~\text{sea})=1\)

Mutual information

The amount of information to be communicated depends on how likely the different outcomes are:

Mutual Information

The quality of the signal depends on how strictly it covaries with the message:

• \(P(\text{1 lamp}~|~\text{land})=0.8\)
• \(P(\text{2 lamps}~|~\text{sea})=0.8\)
• \(P(\text{land}) = 0.8\)

The Joint Distribution

Mutual information

The Mutual Information between message and signal:

  entropy(c(0.2, 0.8)) +      # message uncertainty
  entropy(c(0.68, 0.32)) -    # signal uncertainty
  entropy(c(0.64, 0.04,       # joint uncertainty
            0.16, 0.16))

## [1] 0.1825

  # bits that could've been could've been communicated
  # with a perfect signal
  entropy(c(0.2, 0.8)) 

## [1] 0.7219

Informativeness?

Informativeness?

## Warning: NAs introduced by coercion

Informativness

Need to compare this to some other kind of signal.

  library("babynames")
  head(babynames, 3)

## Source: local data frame [3 x 5]
## 
##   year sex name    n    prop
## 1 1880   F Mary 7065 0.07238
## 2 1880   F Anna 2604 0.02668
## 3 1880   F Emma 2003 0.02052

  tail(babynames, 3)

## Source: local data frame [3 x 5]
## 
##   year sex   name n      prop
## 1 2013   M Zymari 5 2.499e-06
## 2 2013   M Zymeer 5 2.499e-06
## 3 2013   M  Zyree 5 2.499e-06

Comparative Informativeness

Bayesian Update

One off update: